Sums#7719
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Sums

1 second
128 megabytes
Easy

Given an integer , express it as the sum of at least two consecutive positive integers. For example:

If there are multiple solutions, output the one with the smallest possible number of summands.

Input

The first line contains the number of test cases . Each test case consists of one line containing an integer n~(1 \le n \le 10^9).

Output

For each test case, output a single line containing the equation in the format:

n = a + (a + 1) + \ldots + b

as in the example. If there is no solution, output a single word IMPOSSIBLE instead.

Examples

Example 1

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